U.S. Pat. No. 3,279,879 to W. E. Long, dated Oct. 18, 1966, describes a bi-focal corneal lens of the above-described type, in which the lens is self oriented by providing the lower portion of the lens of greater weight than the upper portion, this being achieved by locating the center of curvature of the exterior distant-vision curve downwardly from the optical axis of the lens, so as to make the distant-vision segment thinner than the near-vision segment. However, the border edge of the lens of this Patent is tapered throughout, so that the lower lid has a tendency to overlap the lower border of the lens and the lens will not always be upwardly displaced with respect to the cornea for near vision. Furthermore, the lens in accordance with this Patent, together with already-known bi-focal corneal lenses already on the market, are of limited applications, because of their limited range of parameters.